منابع مشابه
Approximating Spanning Trees with Low Crossing Number
We present a linear programming based algorithm for computing a spanning tree T of a set P of n points in IR, such that its crossing number is O(min(t log n, n1−1/d)), where t the minimum crossing number of any spanning tree of P . This is the first guaranteed approximation algorithm for this problem. We provide a similar approximation algorithm for the more general settings of building a spann...
متن کاملOn Spanning Trees with Low Crossing Numbers
Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( √ n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more general setting), point at some methods for constructing such a tree, and describe some algorithmic...
متن کاملLow-Crossing Spanning Trees - An Alternative Proof and Experiments
We give a quick proof that any planar n-point set has a spanning tree with crossing number O( √ n). Our proof relies on an LP-based approach by HarPeled [8], and it uses Farkas’ lemma. We also present a new heuristic for computing a spanning tree with low crossing number and compare it experimentally with other known approaches.
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 1991
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/1991250201031